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Math Help - Triple Integral and where to start

  1. #1
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    Triple Integral and where to start

    I'm not looking for an answer, more or less where to start.

    Here is the integral:

    6/(1 + 48z - z^3) dzdydx

    I can't tell where to start with this one besides pulling the 6 out of the numerator as a constant. I looked through all sorts of integration thechniques and I found no luck.
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    Quote Originally Posted by markmil2002 View Post
    I'm not looking for an answer, more or less where to start.

    Here is the integral:

    6/(1 + 48z - z^3) dzdydx

    I can't tell where to start with this one besides pulling the 6 out of the numerator as a constant. I looked through all sorts of integration thechniques and I found no luck.
    Taking the 6 out is a good first start. One way of approaching this problem is partial fractions. You'll have 3 fractions left which you can integrate over all three variables one by one, then add the results back together.
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    Look at the denominator. You can't just split the denominator into 3 parts. The whole denominator for that fraction is (1+48z-z^3) The only part of the numerator is the 6.
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    Quote Originally Posted by markmil2002 View Post
    Look at the denominator. You can't just split the denominator into 3 parts. The whole denominator for that fraction is (1+48z-z^3) The only part of the numerator is the 6.
    It isn't trivial to do, but by partial fractions decomposition you can. I am not saying you will get 1/1 +1/48z - 1/z^3. This method is usually covered in a calculus 2 course.

    Partial fraction - Wikipedia, the free encyclopedia
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    Quote Originally Posted by markmil2002 View Post
    I'm not looking for an answer, more or less where to start.

    Here is the integral:

    6/(1 + 48z - z^3) dzdydx

    I can't tell where to start with this one besides pulling the 6 out of the numerator as a constant. I looked through all sorts of integration thechniques and I found no luck.
    You haven't given any integral terminals. Depending on what they are things might be a lot simpler ....
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    Well, I didn't give any because I wanted to know how to start. I don't see a way to split it up for partial fractions though. Especially since it's a 3rd degree, 1st degree, and zero degree. The quardratic equation doesn't work, and I don't see a way to make a perfect square either.
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  7. #7
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    Quote Originally Posted by markmil2002 View Post
    Well, I didn't give any because I wanted to know how to start. I don't see a way to split it up for partial fractions though. Especially since it's a 3rd degree, 1st degree, and zero degree. The quardratic equation doesn't work, and I don't see a way to make a perfect square either.
    Let me blunter than my previous post:

    Your question cannot be answered properly unless you also give the integral terminals. Perhaps you should review some examples from your textbook or class notes to see why that's the case.

    Here's an example of a double integral that illustrates my point:

    Find \int \int \frac{\sin y}{y} \, dy \, dx.

    Find \int_{x = 0}^{x=1} \int_{y = 0}^{y = x} \frac{\sin y}{y} \, dy \, dx.
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    Well I don't think the limits will necessarily change things, but the limits for the first integral are 0 and y. 0 being the lower limit and y being the upper limit. The next integral has limits of x and 4, followed by the third integral having limits of 0 and 4.
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  9. #9
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    Quote Originally Posted by mr fantastic View Post
    Let me blunter than my previous post:

    Your question cannot be answered properly unless you also give the integral terminals. Perhaps you should review some examples from your textbook or class notes to see why that's the case.

    Here's an example of a double integral that illustrates my point:

    Find \int \int \frac{\sin y}{y} \, dy \, dx.

    Find \int_{x = 0}^{x=1} \int_{y = 0}^{y = x} \frac{\sin y}{y} \, dy \, dx.
    I also looked at changing it to cylindrical and spherical. Niether one seems to make things easier though.
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    Quote Originally Posted by markmil2002 View Post
    I also looked at changing it to cylindrical and spherical. Niether one seems to make things easier though.
    Is this triple integral the specific question you've been asked to solve or is it the result of a calculation you've done in order to answer a different question?
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  11. #11
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    It's a triple integral I am trying to solve.
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  12. #12
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    Quote Originally Posted by markmil2002 View Post
    It's a triple integral I am trying to solve.
    Yes I know that. What I'm asking is were you given it to solve or is it the result of trying to solve another question.
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    Just trying to solve it. It was given to me just to solve. It has nothing to do with anything else.
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    Thumbs down

    I guess nobody can help?
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  15. #15
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    Quote Originally Posted by markmil2002 View Post
    I guess nobody can help?
    I'd suggest reversing the order of the integration but the difficulties remain.

    Perhaps you could ask the person who gave you the question exactly how they were expecting you to solve it.

    Personally, I doubt there's a closed form solution.
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